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An analysis of a fractal Michaelis-Menten curve

Published online by Cambridge University Press:  17 February 2009

Jack Heidel  and
John Maloney
Jack Heidel
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182
John Maloney
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182
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Abstract

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Simple chemical reactions can be described by the Michaelis-Menten response curve relating the velocity V of the reaction and the concentration [S] of the substrate S. To handle more complicated reactions without introducing general polynomial response curves, the rate constants can be considered to be scale dependent. This leads to a new response curve with characteristic sigmoidal shape. But not all sigmoidal curves can be accurately fit with three parameters. In order to get an accurate fit, the lower part of the ∫ shaped curve cannot be too shallow and the upper part can't be too steep. This paper determines an exact mathematical expression for the steepness and shallowness allowed.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 3 , January 2000 , pp. 410 - 422
Copyright
Copyright © Australian Mathematical Society 2000

References

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